From U.S. Pat. No. 3,801,978 a monitoring or alarm system is known having two sensors located in one room and working according to the Doppler principle, said sensors responding to at least two physical phenomena of different nature but occurring inevitably in every event of alarm, and covering the same monitoring zone. An increased degree of safety is achieved with this known system in comparison to conventional commercial alarm systems. But in spite of this there is still a considerable susceptibility to sabotage and a high error rate.